Hilbert Space Fragmentation in a Rydberg Quantum Simulator

Programmable Rydberg atom arrays offer rich possibilities for exploring quantum many-body dynamics. When an atom is excited to the Rydberg state, the blockade of nearby atoms leads to constrained dynamics, such as that in the effective PXP model. Complementary to the Rydberg blockade is facilitation, where a Rydberg atom must be present so as to drive other nearby atoms to the Rydberg state.

In this talk, I will present our results on using both blockade and facilitation to impose kinetic constraints on a Rydberg atom array, thereby realizing a broad class of models where the Hilbert space has been shattered into exponentially many disjointed subspaces. First, we uncover a general version of quantum many-body scarring starting from Z_{2k}-ordered initial states. In addition, we find that quantum thermalization proceeds in a way that is restricted to a particular Hilbert space fragment. Notably, thermalization between states belonging to different subspaces is precluded, even when these states have the same energy, defying expectations from the eigenstate thermalization hypothesis.